The viscous Holmboe instability for smooth shear and density profiles. (arXiv:1911.09961v1 [physics.flu-dyn])

The Holmboe wave instability is one of the classic examples of a stratified shear instability, usually explained as the result of a resonance between a gravity wave and a vorticity wave. Historically, it has been studied by linear stability analyses at infinite Reynolds number, $Re$, and by direct numerical simulations at relatively low $Re$ in…

Local wellposedness of the modified KP-I equations in periodic setting with small initial data. (arXiv:1911.09767v1 [math.AP])

We prove local well-posedness of partially periodic and periodic modified KP-I equations, namely for $\partial_t u+(-1)^{\frac{l+1}{2}}\partial^l_x u-\partial_x^{-1}\partial_y^2 u+u^2\partial_x u=0$ in the anisotropic Sobolev space $H^{s,s}(\mathbb{R}\times \mathbb{T})$ if $l=3$ and $s>2$, in $H^{s,s}(\mathbb{T}\times \mathbb{T})$ if $l=3$ and $s>\frac{19}{8}$, and in $H^{s,s}(\mathbb{R}\times \mathbb{T})$ if $l=5$ and $s>\frac{5}{2}$. All three results require the initial data to be small.

Geo-clustered chronic affinity: pathways from socio-economic disadvantages to health disparities. (arXiv:1911.09769v1 [cs.CY])

Our objective was to develop and test a new concept (affinity) analogous to multimorbidity of chronic conditions for individuals at census tract level in Memphis, TN. The use of affinity will improve the surveillance of multiple chronic conditions and facilitate the design of effective interventions. We used publicly available chronic condition data (Center for Disease…

Character expansion of Kac-Moody correction factors. (arXiv:1911.09770v1 [math.RT])

A correction factor naturally arises in the theory of p-adic Kac–Moody groups. In this paper, we expand the correction factor into a sum of irreducible characters of the underlying Kac–Moody algebra. We derive a formula for the coefficients, which lie in the ring of power series with integral coefficients. In the case that the Weyl…

Multi-model mimicry for model selection according to generalised goodness-of-fit criteria. (arXiv:1911.09779v1 [stat.ME])

Selecting between candidate models is at the core of statistical practice. As statistical modelling techniques are rapidly evolving, the need for similar evolution in the ways to select between candidate models is increasing. With Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) not applicable for all sets of candidate models, and likelihood not the…

Minority Voter Distributions and Partisan Gerrymandering. (arXiv:1911.09792v1 [cs.CY])

Many people believe that it is disadvantageous for members aligning with a minority party to cluster in cities, as this makes it easier for the majority party to gerrymander district boundaries to diminish the representation of the minority. We examine this effect by exhaustively computing the average representation for every possible $5\times 5$ grid of…

Multiple Points of Gaussian Random Fields. (arXiv:1911.09793v1 [math.PR])

This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The result is applicable to fractional Brownian sheets and the solutions of systems of…

Robust Learning-based Predictive Control for Constrained Nonlinear Systems. (arXiv:1911.09827v1 [eess.SY])

The integration of machine learning methods and Model Predictive Control (MPC) has received increasing attention in recent years. In general, learning-based predictive control (LPC) is promising to build data-driven models and solve the online optimization problem with lower computational costs. However, the robustness of LPC is difficult to be guaranteed since there will be uncertainties…

Differentiable Algorithm for Marginalising Changepoints. (arXiv:1911.09839v1 [cs.LG])

We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables other than changepoints. Also, it runs in time O(mn) where n is the number of time steps and m the…

Adversarial Risk Analysis for First-Price Sealed-Bid Auctions. (arXiv:1911.09851v1 [stat.AP])

Adversarial Risk Analysis (ARA) is an upcoming methodology that is considered to have several advantages over game theory. ARA solutions for first-price sealed-bid (FPSB) auctions have been found but only under strong assumptions which make the model somewhat unrealistic. In this paper, we use ARA methodology to model FPSB auctions using more realistic assumptions. We…